I'm in Nihongo, I know. But it's bad grammar.

It should be

Hitori janai o wasurenai. I believe that that's right.

Well it translates to "Don't forget you are not alone" so technically yes, two negative forms are used but they are not contradictory. It's actually a line from a song and as far as I can see the grammar is correct.

Also, from my experience Japanese tends to use double negatives in normal sentence construction. For example while we would say "I'm not doing anything," in Japanese it would be "なにもしていません" which literally translates to "I am not doing nothing." (なにも=nothing, していません=negative gerund form of the verb "to do".

Wasurenai de hitori janai yo

That's a double negative... I'm confused. Or you're using bad grammar.